document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113167>Question 1113167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Brian Costa deposited $20,000 in a new savings account at 12% interest compounded semiannually. At the beginning of year 4, Brian deposits an additional $30,000 at 12% interest compounded semiannually. At the end of 6 years, what is the balance in Brian’s account? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728505 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he deposits 20,000 at 12% interest compounded semi-annually.\r<BR>\n" );
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document.write( "at the beginning of year 4, he deposits an additional 30,000 at 12% compounded semi-annually.\r<BR>\n" );
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document.write( "what is the balance in the account at the end of year 6?\r<BR>\n" );
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document.write( "formula to use is f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period<BR>\n" );
document.write( "n is the number of time periods\r<BR>\n" );
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document.write( "your interest rate is 12% per year compounded semi-annually.<BR>\n" );
document.write( "therefore the periods are semi-annual periods.\r<BR>\n" );
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document.write( "to find the interest rate per time period, take 12% and divide it by 2 compounding periods per year to get 6% per semi-annual period.\r<BR>\n" );
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document.write( "in the formula, it is entered as .06, which is the rate, not the percent rate.\r<BR>\n" );
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document.write( "the number of years needs to be multiplied by 2 to get number of semi-annual periods.\r<BR>\n" );
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document.write( "your first investment is for 6 years, therefore, you are talking 12 semi-annual periods.\r<BR>\n" );
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document.write( "your second investment is for 3 years, therefore, you are talking 6 semi-annual periods.\r<BR>\n" );
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document.write( "the formula is, once again:\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "you get 2 formulas.\r<BR>\n" );
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document.write( "first formula is f = 20,000 * (1 + .06) ^ 12.\r<BR>\n" );
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document.write( "the second formula is f = 30,000 * (1 + .06) ^ 6.\r<BR>\n" );
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document.write( "the total money at the end of the 6th year is:\r<BR>\n" );
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document.write( "20,000 * (1 + .06) ^ 12 plus 30,000 * (1 + .06) ^ 6.\r<BR>\n" );
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document.write( "this results in a total amount at the end of the 6th year equal to 82799.5028\r<BR>\n" );
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document.write( "the spreadsheet output below gives you an idea of what the time period to time period cash flows look like.\r<BR>\n" );
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document.write( "your first investment is made at the beginning of the first year, therefore it is entered in time period 0, which is the beginning of the first year.\r<BR>\n" );
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document.write( "your second investment is made at the beginning of the fourth year, therefore it is entered in time period 8 which is the end of the third year and the beginning of the fourth year.\r<BR>\n" );
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document.write( "the year by year cash flow and future value of cash flow and cumulative sum of future value of cash flow is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/032902.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the trick in the cash flow is to get the time periods right.\r<BR>\n" );
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document.write( "the following table describes what they represent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/032903.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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